## pottersheep 3 years ago Grade 12 math help please!! For what value of b will the polynomial p(x) = -2x^3 + bx^2 - 5x +2 have the same remainder when it is divided by x - 2 and x+1?

1. TAKEBACKMATH

okay I will show you:

2. pottersheep

thank you so much!

3. pottersheep

:(

4. TAKEBACKMATH

thinking

5. pottersheep

oh ok sorry

6. TAKEBACKMATH

sorry, it too late for me I will hand this over to lonesome else?

7. pottersheep

ok

8. pottersheep

thanks anyways

9. Callisto

Here it goes~ Have you learnt remainder theorem yet?

10. Callisto

@pottersheep Are you there??

11. pottersheep

Yes sorry, we have!

12. Callisto

So, let R be the remainder when p(x) is divided by x-2. By remainder theorem, what would you get? I mean p(_) = ...?

13. pottersheep

ok one sec

14. pottersheep

So i'd sub in 2 for x

15. Callisto

Yup!

16. pottersheep

3?

17. pottersheep

sorryryyryryryr

18. pottersheep

Sorry what do I do with the b though?

19. pottersheep

4b -24

20. Callisto

Right, so for p(2), you get p(2) = 4b - 24 = R, agree? (By remainder theorem, p(a) = R , when p(x) is divided by x-a)

21. pottersheep

Right, okay

22. Callisto

And what is the remainder when p(x) is divided by x+1 ?

23. pottersheep

b - 5

24. Callisto

Not really.. Remainder = p(-1) = -2(-1)^3 + b(-1)^2 - 5(-1) +2 = ...?

25. pottersheep

Opps, sorry! I subbed in 1!

26. pottersheep

9??

27. pottersheep

b + 9!

28. Callisto

Yes. Note that the remainder is p(x) = R when p(x) is divided by x-a. Now, p(x) is divided by x+1, so a = -1 in the case. [ x-(-1) = x+1]

29. pottersheep

True, sorry!

30. Callisto

From the question, the polynomial p(x) = -2x^3 + bx^2 - 5x +2 have the same remainder when it is divided by x - 2 and x+1. So, equate the two remainder you got and solve b. Got it?

31. Callisto

Oh.. It's okay!

32. pottersheep

Ohhhhhhhhh, so make them equal to each other?? Yes I get it, thank you!!!!!!

33. Callisto

Yes. Since they have the SAME remainder! You're welcome :)